entries of the table
standing in different rows and different columns, at least two are equal.
for which there exist 
consecutive positive integers whose sum is a prime number.
,
an integer, that lie within the polygon is equal to the sum of the lengths of the segments of lines of the form 
,
,
,
intersects a circle at exactly two points 
and 
.
is extended beyond 
such that 
.
intersect at the point 
.
is cyclic. (4)
ascertain whether among its first 
terms there is a number that ends with four zeros.
straight lines in general position are drawn on the plane. Prove that among the parts into which they divide the plane, there are at least 
triangles
and 
such that 
pupils is organised into 
clubs , so that each club contains 
pupils and no two clubs have the same composition. Prove that there are two clubs which have exactly one common member.
Y by
The cells of the 
cube contain the numbers 
, once each number. Two worms are sent from one corner cube to the opposite corner. Each of them can crawl into a cube adjacent to the edge, while the first can crawl if the number in the adjacent cube differs by 
, the second - if they differ by 
. Is there such an arrangement of numbers that both worms can get to the opposite corner cube?
cube contain the numbers 
, once each number. Two worms are sent from one corner cube to the opposite corner. Each of them can crawl into a cube adjacent to the edge, while the first can crawl if the number in the adjacent cube differs by 
, the second - if they differ by 
. Is there such an arrangement of numbers that both worms can get to the opposite corner cube?This post has been edited 1 time. Last edited by parmenides51, Sep 27, 2024, 1:55 AM
